lean_workbook_plus_6313

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $a^2+b^2+c^2\ge ab+bc+ca$ given $a,b,c$ are positive real numbers.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6313 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ 2 + b ^ 2 + c ^ 2 ≥ a * b + b * c + a * c   :=  by sorry

Source